1.

The gravitational field, due to the 'left over part' of a uniform sphere (from which a part as shown , has been 'removed out') at a very far off point, P , located as shown, would be (nearly) : (##DSH_NTA_JEE_MN_PHY_C07_E03_008_Q01.png" width="80%">

Answer»

`(5)/(6) (GM)/(X^(2))`
`(8)/(9) (GM)/(x^(2))`
`(7)/(8) (GM)/(x^(2))`
`(6)/(7) (GM)/(x^(2))`

Solution :Let mass of smaller sphere (which has to be removed ) is m
Radius = `(R)/(2)` (from figure)
`(M)/((4)/(3) pi R^(3)) = (m)/((4)/(3) pi ((R)/(2))^(3)) rArr m = (M)/(8)`
Mass of the left over part of the sphere
`M. = M - (M)/(8) = (7)/(8) ` M
therefore gravitational field due to the left over part of the sphere
`= (GM.)/(x^(2)) - (7)/(8) (GM)/(x^(2))`


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